Abstract: Smoothed particle hydrodynamics is a Lagrangian meshless partilcle method.It gets superiority in simulation of free surface flow and large deformation problems. But low accuracy of kernel approximation becomes an obstacle for widely applications as particles are distributed disorderly or near a boundary.Adopting Taylor expansion and solving integral equation matrix.a second order kernel approximation method,namely K2_SPH is obtained and discussed.With improvement of kernel approximation,improved numedcal techniques are adopted.such as free surface boundary and solid boundary.They are very important for K2_SPH method.With comparison of standard SPH for nonlinear water wave simulation,K2_SPH improves obviously in free surface simulation and distribution of some variables in total particle system.

Key words: smoothed particle hydrodynamics, K2_SPH, meshless method, nonlinear water wave